深内部地球结构对内核平动振荡本征周期的影响

The influence of deep interior structure on the eigenperiod of inner core′s translational oscillations

地球固态内核的平动振荡是地球的基本简正模之一，又称Slichter模，其本征周期大约为几个小时，与地球内部结构密切相关.为了研究影响内核平动振荡的本征周期与内部结构的依赖关系，本文利用球对称、非自转、弹性和各向同性地球模型（SNREI），通过自由振荡运动方程的数值积分，以地球模型PREM为基础，理论上系统研究了地球内部介质（包括密度、地震波速等）分布异常对Slichter模本征周期的影响.数值结果表明，Slichter模周期随着内外核边界（ICB）密度差的增加以类似于双曲线的特征显著减小，当ICB密度差从597kg·m^-3减小到200kg·m^-3时，周期增大66.44％，当ICB密度差从597kg·m^-3增大到1000kg·m^-3时，周期减小21.48％；Slichter模周期随着核幔边界（CMB）密度差的增大而缓慢增大；相对于PREM，地球模型1066A在ICB和CMB的密度差分别相差45.321％和1.132%，内部地震波速度和密度梯度也存在差异，但是，当密度差减小到1066A模型提供的数值时，得到的Slichter模周期与基于1066A获得的结果（4.599h）非常接近，差异分别只有3.762％和0.037％；表明Slichter模本征周期与地球内部介质的精细结构关系不大，而对ICB的密度差非常敏感.内、外核P波波速分布异常对Slichter模周期的影响基本相当，当内核和外核P波波速均增加5％时，Slichter周期分别减小1.02％和1.69％，P波波速分别减小5％时，Slichter模周期分别增加1.27％和1.847％，内核s波波速分布异常比P波波速分布异常对Slichter模周期的影响小1个量级；与地核相比，地幔中的地震波速异常对Slichter模本征周期的影响小1～2个量级；表明地核中地震波速异常对Slichter模周期的影响很小，目前有关Slichter模周期理论计算的差异主要来自于所采用的地球模型中内核边界的密度差的差异，本文结果可以为Slichter模的研究、探测及其对地球深内部结构的约束提供理论依据.

Abstract The translational oscillation of the solid inner core, which is also called Slichter mode, is one of the fundamental normal modes of the Earth. It has an eigenperiod of several hours which is closely related to the Earth% interior structure. Based on the equations for free oscillations of a spherical, non-rotating, elastic and isotropic （SNREI） Earth, and the PREM Earth model, we systematically investigate the influences on Slichter mode＇s eigenperiod caused by the Earth＇s interior medium （including density and seismic velocity） in theory. The numerical results indicate that the eigenperiod of Slichter mode reduces significantly, approximately following a hyperbola, with the increase of the density difference across the inner-outer core boundary （ICB）. When the density difference reduces from 597 to 200 kg · m^-3 , the eigenperiod increases 66.44%. When the density difference increases to 1000 kg · m^-3, the eigenperiod reduces 21.48%. The eigenperiod of Slichter mode increases slowly with the density difference of the core-mantle boundary （CMB） increasing. Relative to PREM, the density differences of the 1066A model at ICB and CMB are 45. 321% and 1. 132% respectively. The interior seismic velocity and density gradient are also different between the PREM model and 1066A model. When the density difference reduces to the value provided by 1066A model, the results are very close to the value from the 1066A （4. 599 h）, and the differences are 3.762% and 0.037% respectively. The results indicate that the eigenperiod of Slichter mode is extremely sensitive to the density contrast across ICB. The influences caused by abnormal distribution of P-wave velocity in inner core and outer core are nearly the same. When P-wave velocity in inner core and outer core increases 5 %, the eigenperiod reduces 1. 02% and 1. 69% respectively, and when it reduces 5%, the eigenperiod increases 1.27% and 1. 847%. The influence caused by abnormal distribution of S-wave velocity is 1 order of magnitude smaller than that caused by P-wave velocity. The influence caused by abnormal distribution of seismic velocity in mantle is 1 ~2 order of magnitude smaller than that caused in core. The results indicate that the influence caused by abnormal distribution of seismic velocity in core is very small, at present, the differences of calculated Slichter moders eigenperiod come mainly from the different density contrast across the ICB of the adopted Earth model. In this paper, the results can provide a theoretical basis for the researching and detecting of Slichter mode, and constraint for the interior structure of the Earth.